"Dead heading" Sunflowers

We planted a packet of seeds titled "Cutting Mix" sunflowers. We live in central Ohio and the flowers have done quite well. My question is this: The first sunflower that bloomed is approx. 6 inches across the center, and the bees have stopped visiting it, and all the petals have fallen off. It appears that there won't be any seeds, and the stalk has approx. 6 more blooms/buds. Should we chop off the first flower and leave the stalk end exposed, or simply let nature "take it's course"?